Immersed Boundary Method with Artificial Density in Pressure Equation for Modeling Flows Confined by Wall Boundaries

The immersed boundary (IB) method is a promising technique for the numerical simulation of complex microchannel flows. However, numerical tests revealed a loss of wall impermeability for certain flow cases leading to unphysical results when using a standard IB method. To solve this problem, we propose a novel artificial density technique incorporated in the pressure solution for IB methods. The pressure equation is modified by scaled density coefficients in IB domains, which reflects the effect the boundary screening. The proposed model is as simple and efficient as the original IB method, and it can eliminate the spurious velocity penetration. Numerical results are shown to justify this method. Its application to a branched microchannel is also presented in the last part of this study.